WASHINGTON  Senate Democrats said Saturday that they had clinched an agreement on a far-reaching overhaul of the nation’s health care system and forged ahead with efforts to approve the legislation by Christmas over Republican opposition.

As the Senate convened in a blizzard, Democratic leaders hailed a breakthrough that came when Senator Ben Nelson, Democrat of Nebraska, agreed to back the bill after 13 hours of negotiations on Friday, making him the pivotal 60th vote for a measure that President Obama has called his top domestic priority.

“Change is never easy, but change is what’s necessary in America,” Mr. Nelson said at a morning news conference. “And that’s why I intend to vote,” he said, “for health care reform.”

Mr. Obama, appearing on television from the White House, said: “Today is a major step forward for the American people. After nearly a century-long struggle, we are on the cusp of making health care reform a reality in the United States of America.”

The legislation, the most significant overhaul of the nation’s health care system in more than a generation, seeks to extend health benefits to more than 30 million uninsured Americans.

The blinding snow outside the Capitol added to what had already been a chaotic few weeks for the Senate, which has met every day since Nov. 30 and was working through its third consecutive weekend. The sergeant-at-arms had four-wheel-drive vehicles at the ready to bring lawmakers in for votes. And while senators wore the jackets and ties required on the Senate floor, dress shoes gave way to boots.

Mr. Nelson committed his vote after winning tighter restrictions on insurance coverage for abortions, as well as increased federal health care aid for his state.

With Senate leaders increasingly confident that they would pass the bill, Mr. Nelson pointedly warned that he would oppose the final version if negotiations with the House, which approved its bill last month, result in changes that he does not like.

But House liberals are expected to resist some concessions made in the Senate. To secure the votes of centrist holdouts, Senate leaders dropped a proposed government-run health insurance plan, or public option, and an alternate plan to let some people ages 55 to 65 buy coverage through Medicare, both favored by liberals.

Because the Democrats nominally control 60 seats in the Senate  the precise number needed to overcome a Republican filibuster  every senator in the Democratic caucus effectively has veto power over the bill. No Republican is willing to support it.

“The lines are drawn,” said Senator Richard M. Burr, Republican of North Carolina. “He has to get 60 votes. If he doesn’t get 60 votes, the American people win. If he does get them, America’s payback will come in the form of the 2010 elections.”

Not all Democrats have publicly said they will vote for the bill, but Senate leaders and senior White House officials believe they have agreement.

“All Senate Democrats stand shoulder to shoulder with President Obama and the American people, who know that inaction is not an option,” the majority leader, Senator Harry Reid of Nevada, said at a news conference.

Faced with Republican resistance that many Democrats saw as driven more by politics than policy disagreements, Senate Democrats in recent days gained new determination to bridge differences among themselves and prevail over the opposition.

Lawmakers who attended a private meeting between Mr. Obama and Senate Democrats at the White House on Tuesday pointed to remarks there by Senator Evan Bayh, Democrat of Indiana, as providing some new inspiration.

Mr. Bayh said that the health care measure was the kind of public policy he had come to Washington to work on, according to officials who attended the session, and that he did not want to see the satisfied looks on the faces of Republican leaders if they succeeded in blocking the measure.

The measure would extend health benefits by expanding Medicaid and providing subsidies to help moderate-income people buy private insurance. It would require nearly all Americans to obtain insurance or pay financial penalties for failing to do so.

By redrawing the health care sector, the legislation stands to reshape roughly one-sixth of the American economy.

The nonpartisan Congressional Budget Office said the legislation would cost $871 billion over 10 years, with the expense more than offset by revenues from new taxes and fees and by reductions in government spending, particularly on Medicare.

The budget office said the bill would reduce future deficits by $132 billion over that period.

Republicans have accused Democrats of using accounting tricks to hide the true cost of the measure, which they predicted would be huge, particularly if Congress did not follow through with the Medicare cuts.

In place of the public option, the Senate bill would create at least two national insurance plans modeled after those offered to federal workers, including members of Congress. The bill includes a new government-run long-term-care insurance program. And it imposes tight new regulations on the health insurance industry, barring insurers from denying coverage based on pre-existing medical conditions and limiting how much extra they can charge based on age.

Mr. Reid, racing to complete the bill by his self-imposed holiday deadline, on Saturday morning introduced a 383-page package of amendments, including the provisions needed to win Mr. Nelson’s support.

Republicans, who vowed to use every procedural weapon to stop the bill, immediately forced a reading of Mr. Reid’s proposal, which wrapped up shortly before 4 p.m. The Senate adjourned about two hours later on track for a crucial procedural vote at 1 a.m. Monday and a final vote on Christmas Eve.

Negotiations with the House are expected to be completed after New Year’s. Under the deal worked out with Mr. Nelson, health insurance plans would not be required or forbidden to cover abortions, but states could prohibit the coverage of abortions by plans that are offered for sale through new government-regulated marketplaces.

The amendment also includes, solely for Nebraska, a special extension of increased federal contributions to the cost of expanding Medicaid, the state-federal insurance program for the poor.

Mr. Reid introduced his amendment after the Senate easily approved and sent to Mr. Obama a $626 billion military spending bill in an extraordinary session that began before sunrise and reflected the increasingly toxic atmosphere in a chamber that normally prides itself on decorum. Despite the 88 to 10 vote, the Pentagon bill was the focus of some angry partisanship. Republicans, who typically vote in unison for military spending measures, especially at a time when the country is fighting two wars, stalled the bill this week even as money was running out for the Pentagon. It was an effort to throw yet another roadblock in the path of Democrats on health care.

The year-end spending measure also included a two-month extension of jobless pay and health coverage for the unemployed.

For weeks, in floor speeches and news conferences, Republicans have warned ominously that the health care bill would spell disaster, raising taxes and hurting families and small businesses by increasing health care costs over the long term and reducing medical services for older patients.

Senator Olympia J. Snowe, a Maine Republican who had been considered a possible Democratic ally, said she would oppose the measure because it was being rushed. “It is a take-it-or-leave-it package,” she said.

Central to the deal to win Mr. Nelson’s support on the health care package was an agreement on the emotionally charged issue of insurance coverage for abortions. Mr. Nelson wanted air-tight restrictions, but an amendment that he proposed was defeated on Dec. 8.

Under Mr. Reid’s amendment, some health plans receiving federal subsidies could offer coverage for abortion, but they could not use federal money to pay for the procedure. They would have to use money taken from premiums paid by subscribers and would have to keep it separate from federal money.

Two of the Senate’s champions of abortion rights, Senators Barbara Boxer, Democrat of California and Patty Murray, Democrat of Washington, issued a joint statement, saying they were satisfied with the agreement.

“We said we would not accept language that prohibited a woman from using her own private funds for her legal reproductive health care  this compromise meets that test,” they said.

Some anti-abortion groups reacted angrily, including Nebraska Right to Life, which said it had been “betrayed” by Mr. Nelson.

Robert Pear contributed reporting.

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Health »A version of this article appeared in print on December 20, 2009, on page A1 of the New York edition.